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If 5x and 3y are consecutive, does that mean x and y will always b consecutive too?

No. x and y will be consecutive if x=2 and y=3 or x=-1 and y=-2. But in all other cases x and y won't be consecutive, for example, x=5 and y=8.
_________________

Re: If x and y are positive integers, what is the greatest [#permalink]

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01 Aug 2014, 17:25

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This post was BOOKMARKED

Bunuel wrote:

carcass wrote:

If x and y are positive integers, what is the greatest common divisor of x and y?

1) 2x + y = 73 2) 5x – 3y = 1

MMMMMMmm

Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything).

But it seems to be a trap answer......

If x and y are positive integers, what is the greatest common divisor of x and y?

This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

(1) \(2x+y=73\). Suppose GCD(x, y) is some integer \(d\), then \(x=md\) and \(y=nd\), for some positive integers \(m\) and \(n\). So, we'll have \(2(md)+(nd)=d(2m+n)=73\). Now, since 73 is a prime number (73=1*73) then \(d=1\) and \(2m+n=73\) (vice versa is not possible because \(m\) and \(n\) are positve integers and therefore \(2m+n\) cannot equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient.

(2) \(5x-3y=1\) --> \(5x=3y+1\) --> \(5x\) and \(3y\) are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, \(5x\) and \(3y\) don't share any common factor but 1, thus \(x\) and \(y\) also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Answer: D.

Hope it's clear.

Thanks for your exp, Bunuel. That's awesome!!!
_________________

......................................................................... +1 Kudos please, if you like my post

Re: If x and y are positive integers, what is the greatest [#permalink]

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18 Aug 2014, 10:57

Bunuel wrote:

\(5x-3y=1\) --> \(5x=3y+1\) --> \(5x\) and \(3y\) are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, \(5x\) and \(3y\) don't share any common factor but 1, thus \(x\) and \(y\) also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Hope it's clear.

Hi Bunuel, Although 5x and 3y are consecutive integers and co-prime , why are x and y co-prime? is it because 5 and 3 are also co-prime?

\(5x-3y=1\) --> \(5x=3y+1\) --> \(5x\) and \(3y\) are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, \(5x\) and \(3y\) don't share any common factor but 1, thus \(x\) and \(y\) also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Hope it's clear.

Hi Bunuel, Although 5x and 3y are consecutive integers and co-prime , why are x and y co-prime? is it because 5 and 3 are also co-prime?

Let me ask you a question: if x and y shared any common factor but 1, would 5x and 3y be co-prime? Wouldn't they also share that factor?
_________________

Re: If x and y are positive integers, what is the greatest [#permalink]

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29 Aug 2014, 12:13

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Re: If x and y are positive integers, what is the greatest [#permalink]

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19 Mar 2015, 11:00

Bunuel wrote:

So, \(5x\) and \(3y\) don't share any common factor but 1, thus \(x\) and \(y\) also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Can someone break this down for me? How do we know that because 5x and 3y don't share any common factors other than 1, x and y also won't share any common factors but 1? Is it because 5 and 3 do not share any common factors?

So, \(5x\) and \(3y\) don't share any common factor but 1, thus \(x\) and \(y\) also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Can someone break this down for me? How do we know that because 5x and 3y don't share any common factors other than 1, x and y also won't share any common factors but 1? Is it because 5 and 3 do not share any common factors?

Think of it this way - say, x and y shared a common factor 2. Then 2 would be a factor of 5x as well as 3y. But we are given that 5x and 3y share no common factor. Hence, x and y can share no common factor.
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Re: If x and y are positive integers, what is the greatest [#permalink]

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02 Jun 2015, 03:48

1

This post received KUDOS

1

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If x and y are positive integers, what is the greatest common divisor of x and y?

1. 2x + y = 73 2. 5x – 3y = 1

Another way of solving it .Both x and y are integers . From 1: x =(73-y)/2 .Since x is a integer it implies 73-y =even number .73 is Odd so y is also Odd .X is even so GCM will be 1.Sufficient

From 2 :5x-3y =1 .They are consecutive numbers i.e .odd-even or even -odd .so the GCM in this case =1 .Sufficient

Option D is correct .

Press Kudos if you like the solution.
_________________

Regards, Manish Khare "Every thing is fine at the end. If it is not fine ,then it is not the end "

If x and y are positive integers, what is the greatest common divisor of x and y?

(1) 2x + y = 73 (2) 5x – 3y = 1

Question : GCD of x and y = ?

Statement 1: 2x + y = 73

This statement can give us multiple solutions of x and y but the important part is to notice the value of GCD in each case e.g. (y=1, x=36) GCD = 1 (y=3, x=35) GCD = 1 (y=5, x=34) GCD = 1 (y=7, x=33) GCD = 1 (y=9, x=32) GCD = 1... and so on...

Finally we realize that instead of multiple solutions of x and y, their GCD is consistently 1, Hence SUFFICIENT

Point to Learn: In all such equations with two variable you can realize that the solutions have a harmony i.e. value of variable x changes by co-efficient of y and value of y changes by co-efficient of x and this relation holds true in all such equation where the GCD of co-efficients of x and y is 1.

If there is some common factor among co-efficients of x and y then cancel the common factor and the rule holds true in those cases with modified equation.

_________________

Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html

Re: If x and y are positive integers, what is the greatest [#permalink]

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16 Mar 2016, 04:29

Here is what i did => i made the pairs of values and saw the pattern and then compiled that D is correct still not able to see a proper solution on this page some are quoting algebra and some are doing by values putting maybe chetan2u will be helpful here.. Any other methods?
_________________

Here is what i did => i made the pairs of values and saw the pattern and then compiled that D is correct still not able to see a proper solution on this page some are quoting algebra and some are doing by values putting maybe chetan2u will be helpful here.. Any other methods?

It explains the best way to deal with this question.

If you want to avoid algebra, think about it like this:

If x and y are positive integers, what is the greatest common divisor of x and y?

1) 2x + y = 73 Say, x and y have a common factor f other than 1. If that is the case, you should be able to take f common out of the two terms on left hand side. So you will get f*something = 73 But 73 cannot be written as product of two numbers other than 1 and itself. So f MUST BE 1. Hence greatest common divisor of x and y MUST BE 1. Sufficient

2) 5x – 3y = 1 Here, 5x and 3y are consecutive integers (since difference between them is 1). Consecutive integers can share no common factor other than 1. So 5x and 3y have no common factors. This means that x and y can have no common factors (other than 1) too. Else that factor would have been common between 5x and 3y too. Hence greatest common divisor of x and y MUST BE 1. Sufficient

Re: If x and y are positive integers, what is the greatest [#permalink]

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22 Apr 2016, 03:23

Bunuel wrote:

carcass wrote:

If x and y are positive integers, what is the greatest common divisor of x and y?

1) 2x + y = 73 2) 5x – 3y = 1

MMMMMMmm

Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything).

But it seems to be a trap answer......

If x and y are positive integers, what is the greatest common divisor of x and y?

This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

(1) \(2x+y=73\). Suppose GCD(x, y) is some integer \(d\), then \(x=md\) and \(y=nd\), for some positive integers \(m\) and \(n\). So, we'll have \(2(md)+(nd)=d(2m+n)=73\). Now, since 73 is a prime number (73=1*73) then \(d=1\) and \(2m+n=73\) (vice versa is not possible because \(m\) and \(n\) are positve integers and therefore \(2m+n\) cannot equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient.

(2) \(5x-3y=1\) --> \(5x=3y+1\) --> \(5x\) and \(3y\) are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, \(5x\) and \(3y\) don't share any common factor but 1, thus \(x\) and \(y\) also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Answer: D.

Hope it's clear.

Hi Bunuel,

Please help me understand - is it that even if two numbers' multiples are co primes, that the numbers themselves will be co primes as well? How? Thank you.

If x and y are positive integers, what is the greatest common divisor of x and y?

1) 2x + y = 73 2) 5x – 3y = 1

MMMMMMmm

Here I'm not sure that the answer is C because is true that we need of both statement to find possible values for X and Y. Infact statement 1 and 2 we do not have values for the variables (can be everything).

But it seems to be a trap answer......

If x and y are positive integers, what is the greatest common divisor of x and y?

This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

(1) \(2x+y=73\). Suppose GCD(x, y) is some integer \(d\), then \(x=md\) and \(y=nd\), for some positive integers \(m\) and \(n\). So, we'll have \(2(md)+(nd)=d(2m+n)=73\). Now, since 73 is a prime number (73=1*73) then \(d=1\) and \(2m+n=73\) (vice versa is not possible because \(m\) and \(n\) are positve integers and therefore \(2m+n\) cannot equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient.

(2) \(5x-3y=1\) --> \(5x=3y+1\) --> \(5x\) and \(3y\) are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, \(5x\) and \(3y\) don't share any common factor but 1, thus \(x\) and \(y\) also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Answer: D.

Hope it's clear.

Hi Bunuel,

Please help me understand - is it that even if two numbers' multiples are co primes, that the numbers themselves will be co primes as well? How? Thank you.

Can you please give an example of what you mean?
_________________

Re: If x and y are positive integers, what is the greatest [#permalink]

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22 Apr 2016, 03:55

This is a classic "C trap" question: "C trap" is a problem which is VERY OBVIOUSLY sufficient if both statements are taken together. When you see such question you should be extremely cautious when choosing C for an answer.

(1) \(2x+y=73\). Suppose GCD(x, y) is some integer \(d\), then \(x=md\) and \(y=nd\), for some positive integers \(m\) and \(n\). So, we'll have \(2(md)+(nd)=d(2m+n)=73\). Now, since 73 is a prime number (73=1*73) then \(d=1\) and \(2m+n=73\) (vice versa is not possible because \(m\) and \(n\) are positve integers and therefore \(2m+n\) cannot equal to 1). Hence we have that GCD(x, y)=d=1. Sufficient.

(2) \(5x-3y=1\) --> \(5x=3y+1\) --> \(5x\) and \(3y\) are consecutive integers. Two consecutive integers are co-prime, which means that they don't share ANY common factor but 1 (for example 20 and 21 are consecutive integers, thus only common factor they share is 1). So, \(5x\) and \(3y\) don't share any common factor but 1, thus \(x\) and \(y\) also don't share any common factor but 1. Hence, GCD(x, y) is 1. Sufficient.

Answer: D.

Hope it's clear.[/quote]

Hi Bunuel,

Please help me understand - is it that even if two numbers' multiples are co primes, that the numbers themselves will be co primes as well? How? Thank you.[/quote]

Can you please give an example of what you mean?[/quote]

In the explanation of the second AC, you state that 5x and and 3y dont share any other common factor other than 1 (since they are co prime), and hence x and y would also be co prime. I tried the same with an example for x and y, 2 and 3 respectively and the equation holds true. But would 5x=3y+1 result in x and y as co prime for all values of 5x=3y+1?

In the explanation of the second AC, you state that 5x and and 3y dont share any other common factor other than 1 (since they are co prime), and hence x and y would also be co prime. I tried the same with an example for x and y, 2 and 3 respectively and the equation holds true. But would 5x=3y+1 result in x and y as co prime for all values of 5x=3y+1?

Let me ask you a question: if x and y shared any common factor but 1, would 5x and 3y be co-prime? Wouldn't they also share that factor?
_________________

If x and y are positive integers, what is the greatest [#permalink]

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22 Apr 2016, 04:11

Bunuel wrote:

abypatra wrote:

In the explanation of the second AC, you state that 5x and and 3y dont share any other common factor other than 1 (since they are co prime), and hence x and y would also be co prime. I tried the same with an example for x and y, 2 and 3 respectively and the equation holds true. But would 5x=3y+1 result in x and y as co prime for all values of 5x=3y+1?

Let me ask you a question: if x and y shared any common factor but 1, would 5x and 3y be co-prime? Wouldn't they also share that factor?

No they would not be co primes then... Understood. Thank you for helping me understand